In the past ten years, there has been significant progress in solid-state optical refrigeration, causing a renewed interest in the possibility of electroluminescent cooling (ELC) in light emitting diodes (LEDs). More recently, our work on III-As based intracavity double diode structures (DDSs) indicates that the threshold for ELC can be reached, in practice, at high powers and 300K if certain non-radiative recombination mechanisms and photodetector (PD) losses are minimized. The studied DDSs consist of a LED, incorporating a high-quality GaAs active layer, optically coupled to a GaAs p-n homojunction PD. Both the LED and PD are integrated in a single device, offering a unique environment for studying ELC. In this paper, we provide a brief overview of the DDS characteristics and investigate the impact of non-radiative interface recombination on the LED, showing how the choice of the barrier layer materials can suppress this effect. We use experimental characterization techniques to calibrate numerical simulations, coupling the drift-diffusion model for charge transport to a photon transport model. To explore the interface effects, we compare DDSs with either GaInP/GaAs or AlGaAs/GaAs double heterojunctions. The results suggest that GaInP barriers allow interface recombination suppression that is sufficient to reach internal cooling in the LED.